Voltammetric systems for assaying biological analytes

ABSTRACT

The present invention relates to systems, methods, and devices for determining the concentration of an analyte in a sample. The use of linear, cyclic, or acyclic voltammetric scans and/or semi-integral, derivative, or semi-derivative data treatment may provide for increased accuracy when determining the concentration of an analyte in a sample. Hematocrit compensation in combination with the data treatments may reduce the hematocrit effect with regard to a glucose analysis in whole blood. In another aspect, fast scan rates may reduce the hematocrit effect.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/495,556, filed Sep. 24, 2014, now allowed, which is a division ofU.S. Nonprovisional application Ser. No. 13/611,557, now U.S. Pat. No.8,871,079, entitled “Voltammetric Systems for Assaying BiologicalAnalytes,” filed Sep. 12, 2012, which is a division of U.S.Nonprovisional application Ser. No. 11/596,309, entitled “VoltammetricSystems for Assaying Biological Analytes,” having a 371(c) date of Sep.7, 2007, now U.S. Pat. No. 8,287,717, which is the National Stage ofInternational Application No. PCT/US05/17009, entitled “VoltammetricSystems for Assaying Biological Analytes,” filed May 16, 2005, and whichclaimed the benefit of U.S. Provisional Application No. 60/571,388,entitled “Methods for Using Linear or Cyclic Voltammetry in AssayingGlucose and Other Biological Analytes,” filed May 14, 2004, each ofwhich is incorporated by reference in its entirety.

BACKGROUND

The quantitative determination of analytes in biological fluids isuseful in the diagnosis and treatment of physiological abnormalities.For example, determining the glucose level in biological fluids, such asblood, is important to diabetic individuals who must frequently checktheir blood glucose level to regulate their diets and/or medication.

Electrochemical methods have been used for such purposes. Anelectrochemical biosensor may use an analyte specific enzyme, such asglucose oxidase or glucose dehydrogenase, to catalyze the oxidation ofglucose in a whole blood sample. During the catalytic oxidation by theenzyme, the redox center of the enzyme accepts the electrons from theanalyte.

This redox center could be the flavin adenine dinucleotide (FAD) ofglucose oxidase, or the enzyme's cofactor such as pyrroloquinolinequinone (PQQ) for the glucose dehydrogenase. The electrons acquired bythe enzyme then may be moved to the electrode by a mediator, which isconverted to a reduced form through oxidation of the enzyme. Finally,the reduced form of the mediator, such as the ferrocyanide species ofthe ferricyanide/ferrocyanide redox pair, is oxidized at the electrodeto generate a measurable current.

This process may be represented by the following equations:Glucose+E_(Ox)==E_(Red)+Product  (1)E_(Red)+nMed_(Ox)==nMed_(Red)+E_(Ox)  (2)Med_(Red)==Med_(Ox)+ne⁻  (3)where E_(Ox) and E_(Red) are the oxidized and reduced forms of the redoxcenter of the enzyme, respectively, while Med_(Ox) and Med_(Red) are theoxidized and reduced forms of the mediator, respectively. The product ofthe enzymatic reaction may be gluconic acid or gluconolactone.

One electrochemical method, which has been used to quantify analytes inbiological fluids, is coulometry. For example, Heller et al. describedthe coulometric method for whole blood glucose measurements in U.S. Pat.No. 6,120,676. In coulometry, the analyte (glucose) concentration isquantified by exhaustively oxidizing the analyte within a small volumeand integrating the current over the time of oxidation to produce theelectrical charge representing the analyte concentration. In otherwords, coulometry captures the total amount of glucose within the sensorstrip.

An important aspect of coulometry is that towards the end of theintegration curve of charge vs. time, the rate at which the chargechanges becomes relatively constant to yield a steady-state condition.This steady-state portion of the coulometric curve forms a relativelyflat plateau region in the curve, thus allowing accurate determinationof the corresponding current. However, the coulometric method requiresthe complete conversion of the entire volume of analyte. As a result,this method is time consuming and does not provide the fast resultswhich users of electrochemical devices, such as glucose-monitoringproducts, demand. Another problem with coulometry is that the smallvolume of the sensor cell must be controlled in order to provideaccurate results, which can be difficult with a mass produced device.

Another electrochemical method which has been used to quantify analytesin biological fluids is amperometry. In amperometry, current is measuredat the end of a period at a constant potential (voltage) across theworking and counter electrodes of the sensor strip. The current is usedto quantify the analyte in the biological sample. Amperometry measuresthe rate at which the electrochemically active species, and thus theanalyte, is being oxidized or reduced. Many variations of theamperometric method for biosensors have been described, for example inU.S. Pat. Nos. 5,620,579; 5,653,863; 6,153,069; and 6,413,411. Theamperometric method samples the analyte concentration near the electrodesurface by measuring the current that is proportional to the diffusionrate and the bulk concentration of the analyte.

A disadvantage of the amperometric method is the non-steady-state natureof the current after applying a potential. The rate of current changewith respect to time is very fast initially and becomes slower as theanalysis proceeds due to the changing nature of the underlying diffusionprocess. Until the consumption rate of the reduced mediator at theelectrode surface equals the diffusion rate, a steady-state currentcannot be obtained. Thus, measuring a current during a non-steady-statetime period may be associated with more inaccuracy than a measurementtaken at a steady-state time period.

One important aspect of measuring analytes in whole blood samples is theeffect of hematocrit. Hematocrit is the volume of red blood cells (RBC)expressed as a percentage of the volume of RBC in a whole blood sample.The hematocrit value for whole blood samples ranges from about 20 to 60%and is typically about 40%.

Reagent biosensors include any system that can detect glucose in a bloodspecimen via an electrochemical reaction. Examples of reagent biosensorsinclude Ascensia AUTODISC® and Elite® biosensors available from BayerHealthCare, LLC of Elkhart, Ind.; Precision® biosensors available fromAbbott in Abbott Park, Ill.; Accucheck® biosensors available from Rochein Indianapolis, Ind.; and OneTouch Ultra® biosensors available fromLifescan in Milpitas, Calif.

Typical electrochemical sensor strips contain a working electrode, acounter electrode, and an optional third electrode. A referencepotential may be provided to the system by the counter electrode, ifconfigured appropriately, or by the optional third electrode. A reagentlayer with an enzyme such as glucose oxidase or glucose dehydrogenaseand a mediator such as ferricyanide or ruthenium hexaamine is printed ordeposited onto the working electrode or onto the working and counterelectrodes with a polymer as the binder.

Examples of polymers used as the binder of the reagents include CMC(carboxyl methyl cellulose) and PEO (polyethylene oxide). The additionof various types and molecular weights of polymers to the reagent layermay assist in filtering red blood cells, preventing them from coatingthe electrode surface.

Preferably, the sensor strip is made by printing electrodes on aninsulating substrate using multiple techniques, such as those describedin U.S. Pat. Nos. 6,531,040; 5,798,031; and 5,120,420. The reagent canbe co-printed onto the working and counter electrodes with a mixture ofa glucose oxidizing enzyme such as glucose oxidase, a mediator such asferricyanide, a hydrophilic polymer such as polyethylene oxide (PEO) andan appropriate buffer, such as a citrate buffer.

Alternatively, a different reagent chemistry can be either printed ormicro-deposited separately onto the working and counter electrodes usingthe method described in a U.S. provisional patent application filed Oct.24, 2003, Ser. No. 60/513,817 with the reagent on the working electrodecontaining the enzyme, the mediator, the polymer and that on the counterelectrode containing a soluble redox species, which could be the same asthe mediator or different, and a polymer. In one embodiment, the polymerused in micro-deposition is carboxyl methyl cellulose.

Examples of suitable bench-top electrochemical instruments which may beused for reading reagent biosensors according to the present inventioninclude, but are not limited to, the BAS 100B Analyzer available fromBAS Instruments in West Lafayette, Ind.; the CH Instrument Analyzeravailable from CH Instruments in Austin, Tex.; the CypressElectrochemical Workstation available from Cypress Systems in Lawrence,Kans.; and the EG&G Electrochemical Instrument available from PrincetonResearch Instruments in Princeton, N.J. Examples of portable instrumentsinclude the Ascensia Breeze® and Elite® meters of Bayer Corporation.

A biosensor for glucose may have an enzyme and a mediator deposited onthe electrodes. The ability of this sensor to measure glucose isaffected as the RBC block the diffusion of the relevant reagents withinthe blood sample. Since the amperometric current is directlyproportional to the diffusion of the reduced form of the mediator, thehematocrit will have a significant impact on the accuracy of the glucosemeasurements. Depending on the hematocrit level in a whole blood sample,the RBC cause a bias in the glucose readings.

Various methods and techniques have been proposed in an attempt toreduce the hematocrit effect of the whole blood on the resulting glucosemeasurements. For example, Ohara et al. in U.S. Pat. No. 6,475,372disclosed a method of using the ratio of currents from a forward and areverse potential pulse to compensate for the hematocrit effect inelectrochemical glucose measurements. McAleer et al. in U.S. Pat. Nos.5,708,247 and 5,951,836 disclosed a reagent formulation using silicaparticles to filter the RBC from the electrode surface, thus reducingthe hematocrit effect. Carter et al. in U.S. Pat. No. 5,628,890disclosed a method of using a wide spacing of the electrodes combinedwith mesh layers to distribute the blood sample for the hematocriteffect.

These conventional techniques for reducing the bias attributable to thehematocrit effect include (a) co-deposition of a polymer to minimize thehematocrit effect, (b) addition of various kinds of fused silica toenforce the filter effect for the polymer layer, (c) compensationcoefficients based on the ratio of currents from a forward and a reversepotential pulse, and (d) self-compensation by utilizing the existingsolution resistance of the whole blood samples. Although these methodsmay be useful, conventional glucose sensors continue to exhibitsignificant analytical bias attributable to the hematocrit effect. Thus,it would be desirable to provide systems for quantifying analytes inbiological fluids, in particular the glucose content of whole blood,which reduces bias from the hematocrit effect.

SUMMARY

In one aspect, the invention provides a method of determining theconcentration of an analyte in a sample that includes applying anacyclic scan to the sample and determining the concentration of theanalyte in the sample.

In another aspect, the invention provides a handheld analyte measuringdevice, for determining the concentration of an analyte in a sample. Theanalyte measuring device includes an acyclic scanning measuring deviceadapted to receive a sensor strip. The acyclic scanning measuring deviceincludes at least two device contacts in electrical communication with adisplay through electrical circuitry. The sensor strip includes at leastfirst and second sensor strip contacts in electrical communication witha working electrode and a counter electrode through conductors, where afirst reagent layer is on at least one of the electrodes and the firstlayer includes an oxidoreductase and at least one species of a redoxpair. Both acyclic and linear scanning measurement devices are provided.

In another aspect, the invention provides a method of determining theconcentration of an analyte in a sample that includes applying avoltammetric forward linear scan to the sample, measuring the resultingcurrents, applying a data treatment to the measured currents, anddetermining the concentration of the analyte in the sample.

In another aspect, the invention provides a handheld measuring device,for determining the concentration of an analyte in a sample, where thedevice is adapted to receive a sensor strip. The device includescontacts, at least one display, and electronic circuitry establishingelectrical communication between the contacts and the display. Theelectronic circuitry comprises an electric charger and a processor inelectrical communication, the processor in electrical communication witha computer readable storage medium comprising computer readable softwarecode. The computer readable software code, when executed by theprocessor, causes the processor to implement semi-integral, derivative,and/or semi-derivative data treatment and/or voltammetric scanning.

In order to provide a clear and consistent understanding of thespecification and claims, the following definitions are provided.

The term “mediator” is defined as a substance that may be oxidized orreduced and that may transfer one or more electrons. A mediator is areagent in an electrochemical analysis and is not the analyte ofinterest, but provides for the indirect measurement of the analyte. In asimplistic system, the mediator undergoes a redox reaction in responseto the oxidation or reduction of the analyte. The oxidized or reducedmediator then undergoes the opposite redox reaction at the workingelectrode and is regenerated to its original oxidation number.

The term “redox reaction” is defined as a chemical reaction between twospecies involving the transfer of at least one electron from a firstspecies to a second species. Thus, a redox reaction includes anoxidation and a reduction. The oxidation half-cell of the reactioninvolves the loss of at least one electron by the first species, whilethe reduction half-cell involves the addition of at least one electronto the second species. The ionic charge of a species that is oxidized ismade more positive by an amount equal to the number of electronstransferred. Likewise, the ionic charge of a species that is reduced ismade less positive by an amount equal to the number of electronstransferred.

The terms “redox pair” are defined as two conjugate species of achemical substance having different oxidation numbers. Reduction of thespecies having the higher oxidation number produces the species havingthe lower oxidation number. Alternatively, oxidation of the specieshaving the lower oxidation number produces the species having the higheroxidation number.

The term “oxidation number” is defined as the formal ionic charge of achemical species, such as an atom. A higher oxidation number, such as(III), is more positive, and a lower oxidation number, such as (II), isless positive.

The term “reversible redox pair” is defined as a pair of redox specieswhere the separation between the forward and reverse scans of thesemi-integral is at most 30 mV at the half-height of the si_(ss)transition. For example, in FIG. 3B the forward and reversesemi-integral scans for the ferricyanide/ferrocyanide redox pair inaddition to the si_(ss) transition height are shown. At the line wherethe half-height si_(ss) transition line intersects the forward andreverse scan lines the separation between the lines is 29 mV,establishing the reversibility of the ferricyanide/ferrocyanide redoxpair at the depicted scan rate.

The term “quasi-reversible redox pair” is defined as a redox pair wherethe separation between the forward and reverse scans of thesemi-integral is larger than 30 mV at the half-height of the si_(ss)transition for the redox pair.

The term “steady-state” is defined as when the change in electrochemicalcurrent with respect to voltage is relatively constant, such as within±10 or ±5%.

The term “reversing-point” is defined as the point in a cyclic oracyclic scan when the forward scan is stopped and the reverse scan isinitiated.

The term “linear scan” is defined as a scan where the voltage is variedin a single “forward” direction at a fixed scan rate, such as from −0.5V to +0.5 V to provide a 1.0 V scan range. A linear scan may beapproximated by a series of incremental changes in potential. If theincrements occur very close together in time, they correspond to acontinuous linear scan. Thus, applying a change of potentialapproximating a linear change may be considered a linear scan.

The term “cyclic scan” is defined as a combination of a linear forwardscan and a linear reverse scan where the scan range includes theoxidation and reduction peaks of a redox pair. For example, varying thepotential in a cyclic manner from −0.5 V to +0.5 V and back to −0.5 V isan example of a cyclic scan for the ferricyanide/ferrocyanide redox pairas used in a glucose sensor, where both the oxidation and reductionpeaks are included in the scan range.

The term “acyclic scan” is defined in one aspect as a scan includingmore of one forward or reverse current peak than the other current peak.For example, a scan including forward and reverse linear scans where theforward scan is started at a different voltage than where the reversescan stops, such as from −0.5 V to +0.5 V and back to +0.25 V, is anexample of an acyclic scan. In another example, an acyclic scan maystart and end at substantially the same voltage when the scan is startedat most ±20, ±10, or ±5 mV away from the formal potential E°′ of theredox pair. In another aspect, an acyclic scan is defined as a scanincluding forward and reverse linear scans that substantially excludethe oxidation and reduction peaks of a redox pair. For example, the scanmay begin, reverse, and end within the steady-state region of a redoxpair, thus excluding the oxidation and reduction peaks of the pair.

The terms “fast scan” and “fast scan rate” are defined as a scan wherethe voltage is changed at a rate of at least 176 mV/sec. Preferable fastscan rates are rates greater than 200, 500, 1000, or 2000 mV/sec.

The terms “slow scan” and “slow scan rate” are defined as a scan wherethe voltage is changed at a rate of at most 175 mV/sec. Preferable slowscan rates are rates slower than 150, 100, 50, or 10 mV/sec.

The term “handheld device” is defined as a device that may be held in ahuman hand and is portable. An example of a handheld device is themeasuring device accompanying Ascensia® Elite Blood Glucose MonitoringSystem, available from Bayer HealthCare, LLC, Elkhart, Ind.

The term “on” is defined as “above” and is relative to the orientationbeing described. For example, if a first element is deposited over atleast a portion of a second element, the first element is said to be“deposited on” the second. In another example, if a first element ispresent above at least a portion of a second element, the first elementis said to be “on” the second. The use of the term “on” does not excludethe presence of substances between the upper and lower elements beingdescribed. For example, a first element may have a coating over its topsurface, yet a second element over at least a portion of the firstelement and its top coating can be described as “on” the first element.Thus, the use of the term “on” may or may not mean that the two elementsbeing related are in physical contact with each other.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1B depict top and end views of the working and counterelectrodes of a typical sensor strip.

FIGS. 2A-2B represent exterior views of the sensor strip of FIGS. 1A-1B.

FIG. 2C is a schematic representation of a measuring device.

FIG. 3A is a graph showing a cyclic voltammogram from a sensor system.

FIG. 3B is a graph of the semi-integral corresponding to the cyclicvoltammogram of FIG. 3A.

FIG. 3C shows an acyclic scan, where the reverse scan is terminatedbefore initiation of the reverse current peak.

FIG. 3D presents the semi-integral of the acyclic data.

FIG. 3E compares a cyclic scan to an acyclic scan, where the forwardscan of the acyclic scan was started near the formal potential E°′ forthe redox pair.

FIG. 3F compares the semi-integral currents of FIG. 3E.

FIG. 3G shows a cyclic scan with an acyclic scan superimposed in thesteady-state region.

FIG. 3H compares the semi-integral and recorded current values for theacyclic scan of FIG. 3G.

FIG. 4A depicts the cyclic voltammogram, semi-integral, andsemi-derivative of 16 mM ferrocyanide in a 20% hematocrit whole bloodsample.

FIG. 4B is an enlargement of the semi-derivative curve of FIG. 4A.

FIGS. 4C-4E depict the semi-derivative curves from the forward linearscan portions of the cyclic voltammograms of FIGS. 7A, 7B and 7C, below.

FIG. 4F depicts the semi-derivative currents from FIGS. 4C-4E.

FIG. 4G depicts a comparison of the calculated glucose values from theunaltered forward scan of the voltammogram (LS), the semi-integral ofthe voltammogram data (si), and the semi-derivative of the voltammogramdata (sd).

FIG. 5 is a set of cyclic voltammograms showing the effect of varyingglucose concentrations in aqueous solutions.

FIG. 6 shows the semi-integral currents of the voltammograms of FIG. 5.

FIGS. 7A-7C are cyclic voltammograms illustrating the effect ofvariations in hematocrit percentage and glucose concentration in wholeblood.

FIGS. 7D-7F are acyclic voltammograms illustrating the effect ofvariations in hematocrit percentage and glucose concentration in wholeblood.

FIGS. 8A-C show the semi-integral currents of FIGS. 7A-7C.

FIGS. 8D-8F show the semi-integral currents of FIGS. 7D-7F.

FIGS. 9A-9C are cyclic voltammograms illustrating the effect of varyingscanning rate on the hematocrit effect.

FIGS. 10A-10C show the semi-integral currents corresponding to thecyclic scans of FIGS. 9A-9C.

FIGS. 11A-11C show the correlation between the semi-integral lines ofFIGS. 10A-10C based on the experimental results of FIGS. 9A-9C and thereference glucose concentration of each sample

FIG. 12 shows a semi-integral current peak and a semi-integral currentsteady-state value, which may be used to determine a Hematocrit Index.

FIG. 13A shows the correlation of the Hematocrit Index with thehematocrit content of whole blood.

FIG. 13B shows the slope of calibration lines of current/glucose(μA/mg/dL) versus %-hematocrit derived from FIG. 11A.

FIG. 14 illustrates the effect of correcting the glucose content (mg/dl)for hematocrit using the hematocrit index.

FIGS. 15A-15C show the derivative currents of the forward scans fromFIGS. 7A-7C plotted versus voltage.

FIG. 16A plots the current at 0.3 volts versus % glucose at 20, 40, and60% hematocrit.

FIG. 16B plots the %-hematocrit versus the ratio of the negative andpositive peaks illustrated in FIG. 15.

FIG. 16C plots the slope of the curves of FIG. 16A versus %-hematocrit.

FIG. 16D shows the effect of correcting glucose content for hematocritusing derivative currents.

FIGS. 17A-17B show the dose response plots for recorded andsemi-integral current values, respectively, of an acyclic scan.

FIG. 17C compares the accuracy of the glucose concentration valuesobtained from the acyclic scan to a cyclic scan having a slow scan rate.

DETAILED DESCRIPTION

An electrochemical analytic system determines the concentration ofanalytes in biological fluids, such as the glucose concentration ofwhole blood. The system includes devices that may apply voltammetriclinear, cyclic, or acyclic scans to a sensor strip containing abiological sample. Voltammetric scans measure currents (amperage) from asensor strip while a potential (voltage) applied to the strip is variedlinearly with time. The devices may compare the resulting current andvoltage data to determine the concentration of the analyte in thesample, while correcting the results for variations in the hematocritcontent of a specific blood sample. The devices also may apply one ormore data treatments, including those based on semi-integration,derivatives, and semi-derivatives to compare and correct thevoltammetric data.

The systems are generally described in the context of determining theconcentration of glucose in a whole blood sample. However, the systemshave other applications where analytes such as cholesterol,triglycerides, lactate, pyruvate, alcohol, bilirubin uric acid, NAD(P)H,and carbon monoxide are found in biological fluids including plasma,urine, saliva and interstitial fluid.

System Overview

The systems for determining analyte concentration may include a sensorstrip for containing the sample and a measuring device for implementingone or more scanning technique and one or more data treatments. In oneaspect, the invention may be a kit including one or more sensor stripand a handheld electronic device for implementing a scanning techniqueand a data treatment to output the concentration of the analyte.

The sensor strip may include a working electrode, a counter electrode,and optionally may include a reference or third electrode. In oneaspect, the working and counter electrodes may be coated with a singlelayer of reagent by co-printing/co-deposition, such as in the Ascensia®AUTODISC sensor. In another aspect, each electrode may be coated with areagent layer optimized for the electrode on which it resides. Thereagent layer at the working electrode includes an enzyme which oxidizesthe glucose in the blood sample and a mediator, such as a redox compoundwhich re-oxidizes the enzyme after it has been reduced by oxidizingglucose. The reduced mediator, which carries electrons from theenzymatic reaction of the glucose oxidation to the electrode, isreoxidized at the surface of the working electrode.

This reoxidation results in the passing of electrons through theelectrodes and the conductors of the sensor strip. The conductors of thesensor strip are in electrical communication with a measurement device,which applies a voltage differential between the electrodes. The devicemay record the current passing through the sensor as a measure of theglucose content of the blood sample.

A whole blood sample is applied to the sensor strip and the glucose inthe blood reacts with the enzyme within or in close proximity to thereagent layer. The diffusion rate of the reduced mediator from thesample to the working electrode may limit the current passing betweenthe working electrode and the counter electrode.

Scanning Techniques

Unlike conventional amperometry and coulometry where a constant voltageis applied while the current is measured as a function of time,voltammetry scanning involves applying a potential (Voltage) across theelectrodes at a fixed rate (V/sec) and measuring the current as afunction of the applied potential. Voltammetry scanning may be performedin a linear, cyclic, or acyclic manner. Cyclic voltammetry scanning iscommonly referred to as “cyclic voltammetry.”

During a linear scan the current at the working electrode is measuredwhile the potential at the working electrode changes linearly with timeat a constant rate. The scan range, such as from −0.5 V to +0.5 V, maycover the reduced and oxidized states of a redox pair so that atransition from one state to the other occurs. The current measured atthe working electrode may be thought of as having three components: theequilibrium current, the diffusion current, and the surface current. Thesurface current, which may derive from any species adsorbed on theelectrode, is generally small and may be neglected. The equilibrium anddiffusion currents are the primary components represented in theresulting voltammogram.

A linear scan voltammogram (a plot of current verses voltage) may becharacterized by a plot that starts at an equilibrium current, reaches apeak current, and decays to a lower current level during the scan. Afterthe initial peak current, the measured current decays and approaches asteady-state region where the oxidation of the reduced mediator at theelectrode surface reaches a maximum rate limited by diffusion. Thus, thesteady-state current at this plateau region of the scan signifies thediffusion-limited current passing through the electrodes, which can beused as a measure of the glucose content of the blood sample.

After completion of the forward scan, for a cyclic or acyclic scan, areversed potential linear scan is applied at substantially the same scanrate as the forward scan. Cyclic, and in some instances, acyclic scansmay examine the transition of a redox species from a reduced state to anoxidized state (and vice versa) in relation to the applied potential orin relation to the diffusion rate of the redox species to the electrodesurface.

In relation to a linear scan, cyclic and acyclic scans may provide abetter representation of the steady-state (diffusion limited) portion ofthe scan. The advantage of cyclic and acyclic scans may be especiallyadvantageous for quantifying the steady-state currents fromquasi-reversible redox pairs at fast scan rates. Additional informationabout linear and cyclic scan voltammetry may be found in“Electrochemical Methods: Fundamentals and Applications” by A. J. Bardand L. R. Faulkner, 1980.

Acyclic scans may have multiple advantages over cyclic scans including ashorter scan time and a substantial decrease in the amount of mediatorelectrochemically converted to the measurable state. Thus, if themediator is reduced in response to the analyte and electrochemicallyoxidized during measurement, terminating the reverse scan before theoxidized mediator is electrochemically reduced decreases the amount ofreduced mediator in the sample not responsive to the analyte. Reducingthe scan time may allow for a shorter analysis time, a significantbenefit for the user.

FIG. 3A presents the data from a 25 mV/sec cyclic scan of aferricyanide/ferrocyanide redox pair as a cyclic voltammogram. Thevoltammogram is characterized by a forward scan peak during the positivevoltage scan from −0.3 V to +0.6 V indicating ferrocyanide oxidation anda reverse scan peak during the negative voltage scan from +0.6 V back to−0.3 V indicating ferricyanide reduction. The forward and reverse scanpeaks center around the formal potential E°′ (−0.05 mV) of theferrocyanide/ferricyanide redox pair, when referenced to thecounter-electrode. In this aspect, the potential of the counterelectrode is substantially determined by the reduction potential offerricyanide, the major redox species present on the counter electrode.FIG. 3B presents the semi-integral of the voltammogram data to show theeffect of this data treatment method on the raw data. FIG. 3C shows acomparable acyclic scan, where the reverse scan is terminated beforeinitiation of the reverse current peak. FIG. 3D presents thesemi-integral of the acyclic scan.

The scanning process leads to increasingly higher currents near theworking electrode as the potential increases relative to the formalpotential E°′. At the same time, oxidation at the electrode surfacegenerates a depleted area and thus a concentration gradient near theelectrode. This concentration gradient creates a driving force foradditional mediator to diffuse toward the electrode. In combination,these forces provide the initial forward peak in the voltammogram as themediator reduced by the analyte or oxidoreductase travels to the workingelectrode and is reoxidized. As the scan continues, the current decaysand approaches the steady-state region, from ˜0.3 to ˜0.6 V in FIG. 3A.The current measured in the steady-state region may be correlated withthe concentration of the reduced mediator, and thus, the glucose contentof the blood sample.

While the potentials where the forward and reverse scans begin (the scanrange) may be selected to span the reduced and oxidized states of theredox pair, the scan range may be reduced to shorten the analysis time.However, the scan range preferably includes the steady-state region forthe redox pair. For example, at a scan rate of 25 mV/sec, theconcentration of the reduced [Red] and oxidized [Ox] species of theferrocyanide/ferricyanide reversible redox pair and the resultingelectrode potential are described by the Nernst equation as follows.

$E = {E^{0^{\prime}} + {\frac{RT}{n\; F}\ln\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}\underset{\_}{\underset{\_}{T = {25{^\circ}\mspace{14mu}{C.}}}}\mspace{14mu} E^{0^{\prime}}} + {\quad{{\frac{0.059}{n}\log\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}\underset{\_}{\underset{\_}{{n = 1}\mspace{11mu}}}E^{0^{\prime}}} + {0.059\;\log\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}}}}}$

When the potential at the working electrode is referenced to its ownredox potential, the formal potential E°′ will become substantially zeroand the equation collapses to:

$\begin{matrix}{E = {{0.059\;\log\frac{\lbrack{Ox}\rbrack}{\lbrack{Red}\rbrack}} = {0.059\;\log{\frac{\lbrack {{Fe}({CN})}_{6}^{- 3} \rbrack}{\lbrack {{Fe}({CN})}_{6}^{- 4} \rbrack}.}}}} & (1)\end{matrix}$From equation (1), when the ratio of the oxidized mediator to thereduced mediator changes by 10, the potential at the working electrodechanges by about 60 mV. The reverse is also true. Thus, for ferricyanide[Ox] to ferrocyanide [Red] concentration ratios of 10:1, 100:1, 1000:1and 10,000:1, the potential at the working electrode will beapproximately 60, 120, 180, and 240 mV away from the zero potential,respectively.

Thus, when the ratio of ferricyanide to ferrocyanide is ˜1000:1, a scanrange of +180 mV to −180 mV would provide substantially completeoxidation of the reduced species at the working electrode. At 180 mV,the oxidation rate is limited by how fast the reduced form of themediator can diffuse to the electrode surface, and from this potentialforward, there exists a diffusion-limited steady-state current region.Thus, if the reversing point is set ˜400 mV from the zero potential,˜200 mV of steady-state region may be provided.

For reversible systems, it may be preferable to provide a scan range offrom 400 to 600 mV, thus scanning from 200 to 300 mV on each side of theformal potential E°′ of the redox pair. For quasi-reversible systems, itmay be preferable to provide a scan range of from 600 to 1000 mV, thusscanning from 300 to 500 mV on each side of the formal potential E°′ ofthe redox pair. The larger scan range may be preferred forquasi-reversible systems because the steady-state portion of the scanmay occur where the plateau region of the scan is not as wide. Inaddition to redox pairs that are inherently quasi-reversible, fast scanrates may cause a redox pair that is reversible at slow scan rates todemonstrate quasi-reversible behavior. Thus, it may be preferable toprovide a larger quasi-reversible scan range for a reversible redox pairat fast scan rates.

Preferably, at least 25, 50, 100, 150, or 300 mV of steady-state regionis provided by the selected scan range. In another aspect, the reversingpoint for a cyclic or acyclic scan is selected so that from 25 to 400mV, from 50 to 350 mV, from 100 to 300 mV, or from 175 to 225 mV ofsteady-state region is provided. For reversible systems, the reversingpoint for a cyclic or acyclic scan may be selected so that from 180 to260 mV or from 200 to 240 mV of steady-state region is provided. Forquasi-reversible systems, the reversing point for a cyclic or acyclicscan may be selected so that from 180 to 400 mV or from 200 to 260 mV ofsteady-state region is provided.

Once the reversing point is selected to provide the desired steady-stateregion, the duration of the reverse scan may be selected for an acyclicscan. As can be seen in FIG. 3E, starting the forward scan andterminating the reverse scan at approximately −0.025 mV resulted in anacyclic scan that included more of the forward current peak than thereverse current peak. From the FIG. 3E comparison, while the peakcurrents obtained for the cyclic (a) and acyclic (b) scans differ, thesteady-state portion of the scans were nearly the same, especially withregard to the reverse scan. When the semi-integral of the scans wereplotted in FIG. 3F, the steady-state current reading of the plateauregion of the return scan was further established, permitting anaccurate current reading in as little as 50 mV from the reversing point.

In another aspect, the reverse scan may be terminated before the reversecurrent peak is reached, as depicted in FIG. 3C. When the forward scanwas started at a potential sufficiently negative, such as at −0.3 mV inFIG. 3C, to the middle of the potential range of the redox pair, such as−0.05 mV in FIG. 3C, the forward scan included the full range of theredox potential of the redox pair. Thus, by terminating the reverse scanat a potential from 50 to 500 mV, from 150 to 450, or from 300 to 400 mVnegative from the reversing point, for example, the reverse current peakmay be excluded for the ferricyanide/ferrocyanide redox pair.

Similarly, the reverse scan also may be terminated before the reversecurrent peak is reached by terminating the scan when the reverse scancurrent deviates in value from the steady-state current. A change in thereverse scan current of at least 2%, 5%, 10%, or 25% may be used toindicate the beginning of the reverse scan current peak.

FIG. 3G compares an acyclic scan that excludes the forward and reverseoxidation peaks of a redox pair with a fast cyclic scan. The acyclicscan rate was fast, 1 V/sec, with starting and ending points of 200 mVand a reversing point of 300 mV. Preferable scan ranges for acyclicscans within the steady-state region of a redox pair that exclude theforward and reverse oxidation peaks are from 10 to 200 mV, morepreferably from 50 to 100 mV.

As seen in the graph, the current values recorded for the acyclic scanare numerically smaller than those of the cyclic scan, while thebackground current is lower for the acyclic scan. This beneficialbackground reduction was unexpectedly obtained without having toinitiate the acyclic scan in the reduction peak portion of the cyclicscan. Thus, a fast and short acyclic scan within the steady-state regionof a redox pair may increase the accuracy of analyte determination dueto a reduction in the signal-to-background ratio.

FIG. 3H shows the semi-integral and recorded current values for the 200to 300 mV acyclic scan of FIG. 3G. The decay currents of the scan aretranslated into a steady-state current plateau by the semi-integral datatreatment. The steady-state portion of the semi-integral, for examplethe current value at 300 mV, may be used to determine the analyteconcentration of the sample.

Cyclic and acyclic scans may provide multiple benefits in relation tolinear scans. In one aspect, the portion of the reverse scan from thereversing point to the point where the reverse current peak begins maybe a better representation of the steady-state region than thesteady-state region of the forward scan. The steady-state region of thereverse scan may be a more accurate representation of analyteconcentration for quasi-reversible redox systems or at fast scan ratesbecause the forward scan may not show a distinct steady-state region.This phenomenon was observed in FIG. 10C, for example.

Data Treatment

Through linear, cyclic, or acyclic scanning, the concentration of theanalyte in the sample may be determined. Furthermore, the hematocriteffect on the analyte concentration measurement may be determined. Whilethe data from the scan may be treated in multiple ways to extract thisand other useful information, semi-integral, derivative, andsemi-derivative techniques are preferred at present.

While an overview of these data treatment methods is described below inrelation to glucose analysis, a more in-depth discussion of these datatreatments for electrochemical currents and the related digitalimplementations may be found in Bard, A. J., Faulkner, L. R.,“Electrochemical Methods: Fundamentals and Applications,” 1980; Oldham,K. B.; “A Signal-Independent Electroanalytical Method,” Anal. Chem.1972, 44, 196; Goto, M., Oldham, K. B., “Semi-integral Electroanalysis:Shapes of Neopolarograms,” Anal. Chem. 1973, 45, 2043; Dalrymple-Alford,P., Goto, M., Oldham, K. B., “Peak Shapes in Semi-differentialElectroanalysis,” Anal. Chem. 1977, 49, 1390; Oldham, K. B.,“Convolution: A General Electrochemical Procedure Implemented by aUniversal Algorithm,” Anal. Chem. 1986, 58, 2296; Pedrosa, J. M.,Martin, M. T., Ruiz, J. J., Camacho, L., “Application of the CyclicSemi-Integral Voltammetry and Cyclic Semi-Differential Voltammetry tothe Determination of the Reduction Mechanism of a Ni-Porphyrin,” J.Electroanal. Chem. 2002, 523, 160; Klicka, R, “Adsorption inSemi-Differential Voltammetry,” J. Electroanal. Chem. 1998, 455, 253.

Semi-Integration

Semi-integration of a voltammogram may separate the diffusion-limitedsteady-state current from the hematocrit affected equilibrium current(initial peak). The semi-integral of the experimentally obtainedvoltammetric current i(t) has the following mathematical form:

$\begin{matrix}{{\frac{d^{{- 1}/2}}{{dt}^{{- 1}/2}}{i(t)}} = {{I(t)} = {\frac{1}{\pi^{1/2}}{\int_{0}^{t}{\frac{i(u)}{( {t - u} )^{1/2}}{du}}}}}} & (2)\end{matrix}$where i(t) is the time function of the voltammetric current obtainedduring the scan; I(t) is a transformation and the semi-integral of i(t);u is a transformation parameter; and d^(−1/2)/dt^(−1/2) is thesemi-integration operator.

At a sufficiently high oxidation potential, the steady-statesemi-integral current is given by:I_(lim)=nFAD^(1/2)C (coul/sec^(1/2))  (3)where I_(lim) is the diffusion-limited steady-state current under thecondition of the surface concentration of the oxidizable species beingzero. Note that the unit of semi-integral current is coul/sec^(1/2),which is not the traditional unit for expressing electrical current,which is coul/sec.

For simplicity, I_(lim) is referred to as the steady-statesemi-integration current (SI) with a unit of coul/sec^(1/2). The SIcurrent (coul/sec^(1/2)) is only a half-step integration from current(coul/sec). The half-step integration is fundamentally different fromcoulometry because in coulometry a full integral is applied to the i-tcurve to provide the total charge passing through the electrodes.

Although equation (2) gives a theoretical definition of thesemi-integral, for digital processing the i-t data may be divided into Nequally spaced time intervals between t=0 and t=NΔt. One such digitalprocessing algorithm is given by equation (4) where t=kΔt and u=jΔt, andi is determined at the midpoint of each interval.

$\begin{matrix}{{I( {k\;\Delta\; t} )} = {\frac{1}{\pi^{1/2}}{\sum\limits_{j = 1}^{j = k}\frac{{i( {{j\;\Delta\; t} - {{1/2}\;\Delta\; t}} )}\Delta\; t^{1/2}}{\sqrt{k - j + {1/2}}}}}} & (4)\end{matrix}$

A preferred algorithm for digital processing is given by:

$\begin{matrix}{{I( {k\;\Delta\; t} )} = {\frac{1}{\pi^{1/2}}{\sum\limits_{j = 1}^{j = k}{\frac{\Gamma( {k - j + {1/2}} )}{( {k - j} )!}\Delta\; t^{1/2}{i( {j\;\Delta\; t} )}}}}} & (5)\end{matrix}$where Γ(x) is the gamma function of x, where Γ(1/2)=π^(1/2),Γ(3/2)=1/2π^(1/2), Γ(5/2)=3/2*1/2π^(1/2), etc.

From equation (3) it may be seen that the steady-state semi-integralcurrent lacks the time-dependence factor of conventional amperometricmethods. Thus, the semi-integral current response may be considered aseries of plateau currents, instead of the continuously changingamperometric currents obtained from conventional amperometry. Becausethe semi-integration allows for quantification of the steady-statecurrent, a faster scan rate may be used than when peak currents arequantified. Thus, linear, cyclic, or acyclic voltammetry in combinationwith semi-integration may rapidly generate steady-state currents inresponse to glucose concentrations. In this manner, the disadvantages ofthe long wait times of coulometry and the non-steady-state nature of thecurrent in amperometry may be reduced.

Equation (3) also shows that reversible or quasi-reversible redox pairsare preferred for use with semi-integration. This is because thesemi-integral from a reversible or quasi-reversible redox pair canexhibit a sharp transition from the reduced state to the oxidized state(and vice versa) and a wide steady-state region, thus making thetransition easier to determine. Ferricyanide/ferrocyanide and the +3 and+2 states of ruthenium hexaamine are examples of redox pairsdemonstrating preferred reversible (slow scan) or quasi-reversible (fastscan) behaviors.

Poorly activated electrodes may not provide an acceptable steady-statecondition even with reversible or quasi-reversible redox pairs. Thus,electrode activation procedures, such as those described in U.S. Pat.No. 5,429,735, may be used to achieve the preferred electrode activity.

Semi-Derivative

In addition to semi-integrals, semi-derivatives of a voltammogram alsomay be used to quantify the analyte by measuring the peak of thesemi-derivative. The semi-derivative of the experimentally obtainedvoltammetric current i(t) has the following mathematical forms:

$\begin{matrix}{\frac{d^{1/2}}{{dt}^{1/2}}{i(t)}} & (6) \\{{{\frac{d^{1/2}}{{dt}^{1/2}}{i(t)}} = {\frac{{dI}(t)}{dt} = {\frac{d}{dt}\lbrack {\frac{1}{\pi^{1/2}}{\int_{0}^{t}{\frac{i(u)}{( {t - u} )^{1/2}}{du}}}} \rbrack}}},( {{coul}\text{/}\sec^{3/2}} )} & (7)\end{matrix}$where I(t) is the semi-integral of the time function i(t).

One implementation of a semi-derivative is to take a full stepderivative of the semi-integral, as shown above in equation (7). Unlikethe peak and steady-state plateau regions representing the voltammetricscan in semi-integral plots, semi-derivative plots convert thevoltammetric scan data into a peak centered at the transition of theredox pair. FIG. 4A depicts the cyclic voltammogram, semi-integral, andsemi-derivative of 16 mM ferrocyanide in a 20% hematocrit whole bloodsample. In this instance, the working electrode of the sensor striplacked enzyme and oxidized mediator. FIG. 4B is an enlargement of thesemi-derivative curve of FIG. 4A showing the peak height for the forwardscan. The value of the forward or reverse scan peak height may becorrelated with the analyte concentration of the sample.

Hematocrit Effect

The normal hematocrit range (RBC concentration) for humans is from 20%to 60% and is centered around 40%. The hematocrit effect refers to thedifference (bias) between a reference glucose concentration readingvalue obtained from a reference instrument, such as the YSI 2300 STATPLUS™ available from YSI Inc., Yellow Springs, Ohio, and an experimentalglucose concentration reading obtained from the methods described above.The difference between the reference and experimental readings resultsfrom the varying hematocrit levels between specific whole blood samples.

While the glucose concentration in whole blood samples is the same fordifferent hematocrit levels, in diffusion based analytic methods, suchas amperometry, the higher the hematocrit, the lower the measuredamperometric current. For whole blood hematocrit levels of 20, 40, and60%, the obtained current readings will be different in the order of20%>40%>60% for the same glucose concentration. This difference betweenthe 20% and 60% current readings constitutes the hematocrit bias spanfor glucose readings obtained for the whole blood sample. The inaccuracyin a glucose determination introduced by varying hematocrit levels foreach whole blood sample may constitute a major source of error in theanalysis.

For example, if the experimentally obtained glucose reading is made withreference to the current reading obtained for glucose in plasma and thecalibration method presumes a 40% hematocrit content in the sample, thenthe higher current readings obtained from whole blood samples containing20% hematocrit will translate into a positive bias with regard to the40% calibration line. Similarly, the lower current readings obtainedfrom whole blood samples containing 60% hematocrit will translate into anegative bias with regard to the 40% calibration line.

Hematocrit Reduction

In one aspect, a slow scan rate may be combined with linear, cyclic, oracyclic scanning and semi-integration to reduce the hematocrit bias ofthe concentration determination when whole blood is analyzed for glucoseconcentration. FIG. 10A shows that for a slow 25 mV/sec scan rate alarge peak is observed in the forward scan portion of the semi-integralfor 60% hematocrit (line c), while a smaller peak is observed for 40%hematocrit (line b). The 20% hematocrit line (a) lacks a significantpeak. Thus, the peak portion of the semi-integral plot is responsive tothe hematocrit content of the sample and the magnitude of the peak maybe quantitatively related to the hematocrit level.

In another aspect, linear, cyclic, or acyclic scans may be combined withderivative data treatment to reduce the hematocrit bias of theconcentration determination when whole blood is analyzed for glucoseconcentration. FIGS. 15A-15C depict the derivatives of the cyclicvoltammograms of FIGS. 7A-7C. These derivative plots show an initialincrease in current as voltage increases, followed by a decrease, andfinally a steady-state region. The hematocrit effect may be seen in thenegative peak located at about 0.1 volts in FIGS. 15A-15C, with higherRBC concentrations reflected as more negative peak values.

While the values of the positive and negative derivative peaks, such asthose depicted in the derivative plot of FIG. 15B, areconcentration-dependent, the ratio of the negative peak to the positivepeak cancels out the concentration dependence, thus beinghematocrit-dependent. Because this ratio (HI-DER) is concentrationindependent and hematocrit dependent, the ratio indicates the percenthematocrit in the sample. Thus, this ratio of the derivative peaks maybe used to determine a hematocrit compensation equation for analytedetermination, as described further below.

In another aspect, linear, cyclic, or acyclic scans may be combined withsemi-derivative data treatment to reduce the hematocrit bias of theconcentration determination when whole blood is analyzed for glucoseconcentration. FIGS. 4C, 4D, and 4E depict the semi-derivative curvesfrom the forward linear scan portions of the cyclic voltammograms ofFIGS. 7A, 7B and 7C at 50, 100, and 40 mg/dL glucose after subtractionof the background voltammogram (0 mg/dL glucose).

FIG. 4F depicts the semi-derivative currents from FIGS. 4C, 4D, and 4Eplotted against the reference glucose concentrations at each hematocritlevel. The overlap of the 20% and 40% hematocrit lines establishes thatthe hematocrit effect was substantially eliminated at the lower 20%value. The hematocrit bias between the 40% hematocrit line and the 60%hematocrit line also was reduced in relation to that obtained from thesteady-state portion of the unaltered data from the voltammogram or fromthe semi-integration of the voltammogram. Thus, the semi-derivative datatreatment may inherently provide hematocrit compensation for glucosedetermination.

FIG. 4G depicts a comparison of the data from the unaltered forward scanof the voltammogram (LS), the semi-integral of the voltammogram data(si), and the semi-derivative of the voltammogram data (sd). The glucosevalues were calculated using the calibration curve at the 40% hematocritlevel. As may be seen from the plot, the semi-derivative datacorresponds well to the line obtained from the YSI reference instrument.

Semi-integration and derivative data treatments allow for identificationand quantification of the portion of the current scan affected by thehematocrit effect. Thus, these data treatments allow for a reduction ofthe hematocrit bias that would otherwise affect the determination of theanalyte concentration. Semi-derivative data treatment may allow for areduction of the hematocrit bias that would otherwise affect thedetermination of the analyte concentration without a compensationequation, as discussed further below.

In another aspect, faster scan rates, such as the 500 and 1000 mV/secscan rates of FIGS. 10B and 10C, may be combined with linear, cyclic, oracyclic scanning and semi-integration, derivative, or semi-derivativedata treatment to reduce the hematocrit bias and measure the glucosecontent of whole blood. Faster scan rates also may provide the benefitof shorter scan times, a significant benefit for the user.

When the total length of the scan is relatively long as in conventionalamperometry or slow scan voltammetry, the diffusion of the mediator andthe current measured will be largely affected by the RBC content of thesample. Conversely, if the scan rate is fast, such as 500 mV/sec, thetime required to reach a 400 mV termination point from a −200 mVstarting point is 1.2 seconds. Similarly, the 400 mV termination pointmay be reached after 0.6 seconds at a 1000 mV/sec scan rate or after 0.3seconds at a 2000 mV/sec scan rate. Thus, total scan times of at most 3seconds, 1.5 seconds, 1 second, or 0.5 second may reduce the hematocritbias on the concentration measurement without mathematical removal.

Determining Analyte Concentration

FIG. 5 depicts the effect on the cyclic voltammograms when the glucoseconcentration of an aqueous solution is increased. Lines representingglucose concentrations of 0 mg/dL (line a), 100 mg/dL (line b), 200mg/dL (line c), 400 mg/dL (line d), and 600 mg/dL (line e) are shown.The scanning rate was 25 mV/sec. FIG. 6 presents the scan data from FIG.5 after conversion to semi-integral currents by a semi-integral datatreatment. Thus, difference in each glucose concentration is apparentfrom the X-axis of FIG. 6.

The shape of a cyclic voltammogram will change as the whole blood sampleis scanned. The cyclic voltammogram will show a displacement of thevoltammetric currents that varies with the hematocrit and the glucoseconcentration, especially the currents near the steady-state portion(0.3-0.4 V in FIGS. 7A-7C). The change may be seen in FIGS. 7A-7C wherethe voltammograms are shown for glucose concentrations of 50 mg/dL (7A),100 mg/dL (7B), and 400 mg/dL (7C) respectively, and also for 20, 40,and 60% hematocrit (curves a, b, c respectively) for each of the glucoseconcentrations. The scanning rate was 25 mV/sec. As expected in view ofthe hematocrit effect, the higher the hematocrit percentage in thesample, the greater the reading for the same glucose concentration. Thecorresponding semi-integral plots of the cyclic scans are shown as FIGS.8A-8C, where the displacement between the steady-state currents arehighlighted with a circle. FIGS. 7D-7F and 8D-8F present the scan dataand the corresponding semi-integrals for an analogous acyclic scan.

Scanning may be performed over the range of −600 mV to +600 mV; however,the preferred scan range depends on the redox pair (mediator) used inthe biosensor. Generally, the measuring device will be programmed duringthe manufacturing stage with the range which is to be scanned.

FIGS. 9A-9C depict the results for scanning rates of 25 mV/sec, 500mV/sec, and 1000 mV/sec, respectively, for blood samples containing 400mg/dl of glucose. As the scan rate increases from 25 mV/sec in FIG. 9Ato 500 mV/sec in FIG. 9B and 1000 mV/sec in FIG. 9C, the initialhematocrit affected peak decreases. Furthermore, peak current values arerelated to the hematocrit values of the sample (a is 20%, b is 40%, c is60% hematocrit), with greater hematocrit percent generally correlatingwith faster decay from peak currents at slow scan rates.

The semi-integral plots corresponding to the voltammograms of FIGS.9A-9C are shown as FIGS. 10A-10C, respectively. As seen from the circledreversing points in the 25 mV/sec FIG. 10A scan, the steady-statecurrents of the 20%, 40% and 60% hematocrit lines were separated withregard to the Y-axis. As the scan rates were increased to 500 mV/sec inFIG. 10B and to 1000 mV/sec in FIG. 10C, the Y-axis separation of the20%, 40%, and 60% hematocrit lines decreased. Thus, as the scan rateincreases, the hematocrit affected portion of the scan is diminished.

FIGS. 11A-11C show the correlation between the semi-integral lines ofFIGS. 10A-10C based on the experimental results of FIGS. 9A-9C and thereference glucose concentration of each sample. The reference glucoseconcentration values from the YSI instrument (X-axis) were compared tothe semi-integral currents (Y-axis) for each hematocrit percentage. Asexpected, the 25 mV/sec scan of FIG. 11A shows the largest biasattributable to the hematocrit effect, while the faster 500 and 1000mV/sec scans of FIGS. 11B and 11C, respectively, show less bias.

The ratio of the peak to steady-state current values in a semi-integralplot may be referred to as the Hematocrit Index (HI), which may bedefined as the semi-integral current peak (i_(p)) divided by thesemi-integral current steady-state value (i_(ss)), as shown in FIG. 12.The calculated Hematocrit Index (HI) was correlated with the actual%-hematocrit content of the sample to provide the correlation line shownin FIG. 13A. As previously discussed with regard to a derivative datatreatment, a HI-DER ratio also may be used to provide the correlationline.

A compensation equation that describes the slope or the intercept andthe slope of a correlation line, such as that shown in FIG. 13A for asemi-integral data treatment, may then be determined. Once thecompensation equation is determined, the glucose concentration of thesample, compensated for the hematocrit effect, may be determined byplugging a desired current value, such as the steady-state currentvalue, into the equation. Thus, the ratio of the peak to steady-statecurrent value for semi-integral data treatment, or the ratio of thenegative peak to the positive peak for derivative data treatment, may beused to correct for the analytical bias attributable to the hematocriteffect.

FIG. 13B depicts the correlation between slope and %-hematocrit forvarying glucose concentrations at a fixed current with hematocritcompensation. As may be seen from the graph, the compensation equationdetermined to describe the curve of FIG. 13A provides a substantiallylinear correlation between current and glucose concentration, regardlessof the underlying hematocrit content of the WB sample. FIG. 14 comparesmultiple compensated and un-compensated glucose readings obtained from asensor system of the present invention with the values obtained from theYSI reference instrument.

The following examples are provided to illustrate one or more preferredembodiments of the invention. Numerous variations can be made to thefollowing examples that lie within the scope of the invention.

EXAMPLES Example 1: Preparation of the Sensor Strip

Referring to FIGS. 1A-B, electrodes 12 and 14 were formed on a base ofinsulating material, such as using the techniques described in U.S. Pat.Nos. 5,798,031 and 5,120,420, to prepare an electrochemical sensor strip10. Silver paste 18 was deposited by screen printing onto apolycarbonate strip 16. This paste was printed in a pattern to form theelectrical contacts 20 a and 20 b and the lower layer 18 of theelectrodes 12 and 14.

In FIG. 1B, an ink containing conductive carbon and a binder was thenapplied by screen printing in a pattern 22 and 24 to form the top layerof each electrode, a reagent layer 26 and 28 of glucose oxidase (orPQQ-GDH glucose dehydrogenase) and ferricyanide as a mediator. Theworking and counter electrodes 12 and 14 had surfaces of 1 mm and 1.2mm², respectively, and the electrodes were separated by about 0.25 mm.In FIG. 2A, a dielectric layer 30 containing acrylate-modifiedpolyurethane was deposited onto the base. The lower layers of theelectrodes then were cured with UV radiation.

Referring to FIG. 2B, after drying, the base was bonded to a lid 32 toform the sensor strip 10. The construction of the lid was performed asdescribed in U.S. Pat. No. 5,798,031. A coating solution of an aqueouspolyurethane dispersion was spread on one side of a polycarbonate stripand allowed to dry. The strip was formed into a lid by embossing to formconcave area 34 and by punching hole 36. The lid was bonded to the baseby aligning and contacting the lid and the base, followed by applyingheat to the contact area along the periphery of the structure.

The completed electrochemical sensor was activated using the proceduresdescribed in U.S. Pat. No. 5,429,735 to increase the activity of theelectrode.

Example 2: Performing the Analysis

FIG. 2C is a schematic representation of a measuring device 200including contacts 220 in electrical communication with electricalcircuitry 210 and a display 230. In one aspect, the measuring device 200is adapted to be handheld and to receive a sensor strip. In anotheraspect, the measuring device 200 is a handheld measuring device adaptedto receive a sensor strip and implement voltammetric scanning. Inanother aspect, the measuring device 200 is a handheld measuring deviceadapted to receive a sensor strip and implement acyclic scanning.

The contacts 220 are adapted to provide electrical communication withthe electrical circuitry 210 and the contacts of a sensor strip, such asthe contacts 20 a and 20 b of the sensor strip 10 depicted in FIG. 1A.The electrical circuitry 210 may include an electric charger 250, aprocessor 240, and a computer readable storage medium 245. Theelectrical charger 250 may be a potentiostat or the like. Thus, thecharger 250 may apply a voltage to the contacts 220 while recording theresulting current to function as a charger-recorder.

The processor 240 may be in electrical communication with the charger250, the computer readable storage medium 245, and the display 230. Ifthe charger is not adapted to record current, the processor 240 may beadapted to record the current at the contacts 220.

The computer readable storage medium 245 may be any storage medium, suchas magnetic, optical, semiconductor memory, and the like. The computerreadable storage medium 245 may be a fixed memory device or a removablememory device, such as a removable memory card. The display 230 may beanalog or digital, in one aspect a LCD display adapted to displaying anumerical reading.

When the contacts of a sensor strip containing a sample are inelectrical communication with the contacts 220, the processor 240 maydirect the charger 250 to apply a voltammetric scan to the sample, thusstarting the analysis. The processor 240 may start the analysis inresponse to the insertion of a sensor strip, the application of a sampleto a previously inserted sensor strip, or in response to a user input,for example.

Instructions regarding implementation of the voltammetric scan may beprovided by computer readable software code stored in the computerreadable storage medium 245. The code may be object code or any othercode describing or controlling the functionality described in thisapplication. The data that results from the scan may be subjected to oneor more data treatments in the processor 240 and the results, suchanalyte concentration, output to the display 230. As with the scanninginstructions, the data treatment may be implemented by the processor 240from computer readable software code stored in the computer readablestorage medium 245.

Example 3: Cyclic Voltammetry and Semi-Integration

An 100 mg/dL aqueous glucose solution was introduced into an AscensiaAUTODISC® sensor. A cyclic scan having a 25 mV/sec scan rate was appliedto the sensor strip using a CH Instrument potentiostat. The cyclicvoltammogram (CV) was plotted as FIG. 3A, while its semi-integral (si)was plotted as FIG. 3B. The data was plotted as a function of thescanning potential vs. the potential at the counter electrode(ferricyanide). FIG. 3B further illustrates the plateau of thesteady-state current in the semi-integral plot, where the differencebetween the steady-state plateau region between 0.2 V and 0.4 V, forexample, was substantially zero, while the difference between thesteady-state plateau and the forward current peak (si_(ss)) at ˜−0.15 Vwas relatively large.

The equations used for this semi-integral data treatment, and thederivative and semi-derivative data treatments described elsewhere, wasimplemented with the Electrochemical Workstation software package,version 4.07, revised Apr. 26, 2004, which accompanies the CHInstruments Electrochemical Workstation, model CHI 660A.

Example 4: Effect of Higher Glucose Concentration

In FIG. 5, cyclic scanning was applied to Ascensia AUTODISC® glucosesensor strips loaded with aqueous glucose solutions containing 0, 100,200, 400 and 600 mg/dL glucose, labeled a-e, respectively. As seen inthe FIG., the peak current for each glucose concentration rose andshifted to higher potentials as the glucose concentration increased.FIG. 6 depicts the corresponding semi-integrals for the cyclicvoltammograms of FIG. 5. At zero glucose concentration, thesemi-integral current was substantially zero.

Example 5: Cyclic Voltammetry of Glucose in WB Samples, Slow Scan

As generally described in the U.S. provisional patent application filedon Oct. 24, 2003, Ser. No. 60/513,817, sensor strips were constructedhaving different reagent layers on the working and counter electrodes. Alayer of ferricyanide from a solution of about 22% K₃Fe(CN)₆, 0.7%bentone, 1.5% CMC, but without active ingredients, was deposited on thecounter electrode. A layer was deposited on the working electrode madefrom a reagent solution of 16.8 unit/μL PQQ-GDH, 250 mM ferricyanide,1.8% CMC, 64 mM phosphate and 64 mM NaCl. Whole blood samples containing50 mg/dL glucose and 20%, 40%, or 60% hematocrit (labeled a-c,respectively in FIGS. 7A-7C) were introduced to the sensor strips.

The peak current from the 60% hematocrit sample (c) was the highest, butdecayed the fastest to about the same steady-state current as thesamples including 20% (a) and 40% (b) hematocrit. The current decayprocesses for 60% hematocrit whole blood samples the 50 mg/dLconcentration is similar to that observed in FIGS. 7B and 7C for 100 and400 mg/dL concentrations, respectively. As the glucose concentrationincreased in the 60% hematocrit whole blood samples, the steady-statecurrent value decreased in relation to the current values obtained in20% and 40% hematocrit samples.

Example 6: Semi-Integration of Cyclic Voltammograms

While cyclic and acyclic currents may be used directly to quantify theglucose concentrations of samples, the semi-integrals of thesevoltammograms provide preferable values to represent the glucoseconcentration of the sample. The semi-integrals presented in FIGS. 8A,8B and 8C were obtained from FIGS. 7A, 7B, and 7C. Note thesemi-integrals from the 20% whole blood samples (a) are substantiallyflat with virtually no peak at the plateau. As the hematocrit levelincreased, the peaks became more and more prominent from 40% to 60%hematocrit (b, c). Also as the glucose concentration increased, thethree steady-state currents at 20%, 40% and 60% hematocrit separatedfurther. The steady-state current at 0.3 V from the semi-integral wasused to construct the calibration curves for the three hematocrits.

Example 7: Cyclic Voltammetry of Glucose in WB Samples, Fast Scan

The sensor strips described in Example 4 were used to conduct fast scancyclic voltammetry with whole blood glucose at 20%, 40% and 60%hematocrit levels. FIGS. 9A, 9B, and 9C are cyclic voltammograms ofwhole blood including 400 mg/dL glucose at 0.025 V/sec, 0.5 V/sec and 1V/sec scan rates, respectively. While a large displacement between thevoltammetric currents at 0.3 V for voltammograms at the 0.025 V/sec scanrate existed, this displacement decreased with increased scan rates.Semi-integrals of these cyclic voltammograms are shown in FIGS. 10A,10B, and 10C. The steady-state currents for each hematocrit percentageat the same glucose concentration merged together as the scan rateincreased. The initial current peak was substantially reduced at fastscan rates.

Example 8: Acyclic Voltammetry of Glucose in WB Samples, Fast, ShortScan

Whole blood samples containing 400 mg/dL glucose and 20, 40, or 55%hematocrit were each applied to 3 sensor strips. After an approximate 6second wait, a fast, 1 V/sec acyclic scan was applied from 0.2 V to 0.3V and back to 0.2 V. After determining the semi-integral currents fromthe scans, as previously described with respect to FIG. 3H, the acyclicscan current value and the corresponding semi-integral current value at0.3 V were used to determine the glucose concentration in each of the 3WB samples.

FIGS. 17A-17B show the dose response plots for the recorded current andsemi-integral current values, respectively. In relation to the recordedcurrent values, the semi-integral data treatment of FIG. 17B provided aslight reduction in analytical bias between the 20 and 55% samplesattributable to the hematocrit effect. FIG. 17C compares the accuracy ofthe glucose concentration values obtained from the acyclic scan to thoseobtained from a cyclic scan having a slow scan rate of 0.025 V/sec. Theconcentration values obtained from the acyclic scan are closer to thoseobtained from the reference YSI instrument than those from the longercyclic scan.

Example 9: Calibration Curves of si Currents at Different Scan Rates

Using the semi-integral currents from the 20%, 40%, and 60% hematocritlines, calibration curves were constructed for scan rates of 0.025V/sec, 0.5 V/sec and 1 V/sec, as shown in FIGS. 11A, 11B and 11C. Thesensor strips were similar to those of Example 4. At a scan rate of0.025 V/sec, three distinct lines were observed for the threehematocrits of whole blood samples tested in FIG. 11A. As the scan rateincreased from 0.025 V/sec to 0.5 V/sec (FIG. 11B), the threecalibration lines moved closer together and almost merged at 1 V/sec(FIG. 11C). This example demonstrated that glucose measurements in wholeblood samples may avoid the hematocrit effect of the WB samples.

Example 10: Defining Hematocrit Index from Semi-Integrals

From FIGS. 8A-C, a relationship exists between the hematocrit level andthe height of the current peaks. The ratio of peak height tosteady-state current (si) is independent of the glucose concentration.This characteristic may be used to indicate the hematocrit level in thewhole blood sample.

FIG. 12 defines the Hematocrit Index (HI) as the ratio of the peakcurrent to the steady-state current from the semi-integral. The tablebelow lists the peak and plateau currents of semi-integrals at 50, 100,and 400 mg/dL whole blood glucose and 20%, 40%, and 60% hematocrit.

Peak and Plateau Currents (si): WB glucose 20% 40% 60% mg/dL Peakplateau Peak plateau Peak plateau  50 34.69 34.31 36.94 32.79 42.2531.74 100 44.4  43.88 45.22 40.76 44.58 33.44 400 92.34 93.46 94.7489.16 70.74 56.71 Hematocrit Index (HI): Peak/Plateau Ratio 20% 40% 60% 50 1.01 1.13 1.33 100 1.01 1.11 1.33 400 0.99 1.06 1.25 Ave 1.00 1.101.30 StdDev 0.014 0.033 0.049 %-CV 1.35 3.01 3.75

Example 11: Compensation of Measurement Biases for WB Glucose

The whole blood %-hematocrit was plotted against the hematocrit index(HI) value as a calibration curve for the hematocrit index, as shown inFIG. 13A. At the same time, the slope of the glucose calibration linesat the three hematocrit levels from FIG. 11A was plotted against the WB%-hematocrit, as shown in FIG. 13B. Instead of using the single slope(and intercept) at 40% hematocrit to calculate the glucose values fromthe current signals, %-hematocrit-dependent slope was used. This wasaccomplished in the following manner:

-   -   (a) after the peak and plateau currents from a semi-integral,        such as from FIG. 12 was obtained, the Hematocrit Index (HI)        value was calculated.    -   (b) Using this HI value, the %-hematocrit value of a WB sample        was found from FIG. 13A.    -   (c) Using this %-hematocrit value, an appropriate calibration        slope was determined from FIG. 13B, which is        hematocrit-dependent. A similar method also may be used to find        the hematocrit-dependent intercept.    -   (d) The slope (and intercept) from (c) was then used to convert        the si current into a glucose value.        FIG. 14 shows the final result of such a compensation procedure,        where uncompensated glucose readings are shown as diamonds,        while compensated data points are shown as open squares. The        improvement in accuracy is evident, particularly at higher        glucose concentration.

Example 12: Derivatives of Cyclic Voltammograms

Hematocrit values may be distinguished by the current decay process thatmay follow the peak current in a scan. This feature is shown in FIGS.7A, 7B, and 7C, where the current decay is the fastest in 60% hematocritwhole blood. This feature also may be represented by taking thederivative of the voltammetric currents from the scan. FIGS. 15A-15Cshow the derivatives of cyclic voltammograms at 50 mg/dL, 100 mg/dL, and400 mg/dL, with 20%, 40%, and 60% hematocrit percentages. The largestnegative peak in the derivative curve represents the fastest currentdecay of the cyclic voltammograms of FIGS. 7A-7C. Thus, the peak heightin the derivative diagram may be used to compensate for the analyticalbias due to the hematocrit effect in whole blood. In one aspect, themethod illustrated in FIGS. 16A-16C was used, which is similar to thatdiscussed in Example 9 for semi-integrated currents.

FIG. 16A shows a plot of CV currents at the steady-state region of 0.3volts versus the % glucose at 20, 40, and 60% hematocrit. This issimilar to FIG. 11A for semi-integrals and illustrates the divergence ofthe currents with increasing hematocrit. FIG. 16B shows a plot of theaverage ratio of the negative to positive peaks versus %-hematocrit ofFIGS. 15A-15C. This ratio is another definition of a Hematocrit Index,in this case using derivatives of the current versus voltage rather thanthe semi-integral currents. FIG. 16C shows the slope of the curves ofFIG. 16A versus %-hematocrit. In a similar procedure to that forsemi-integration, derivatives of current versus voltage were obtainedand the negative to positive peaks were used to define a HematocritIndex (HI-DER). The HI-DER was used to determine the %-hematocrit fromFIG. 16B. Then, FIG. 16C was used to correct the measured glucosecontent for the %-hematocrit. FIG. 16D showed the correction for thehematocrit effect using the derivatives of currents obtained byvoltammetry.

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that other embodimentsand implementations are possible within the scope of the invention.Accordingly, the invention is not to be restricted except in light ofthe attached claims and their equivalents.

What is claimed is:
 1. A system for determining a concentration of ananalyte in a sample, comprising: a measuring device including at leasttwo device contacts in electrical communication with a display throughelectrical circuitry, the measuring device being configured to apply anacyclic scan to the sample; and a sensor strip receivable by themeasuring device, the sensor strip including: a first sensor stripcontact; a second sensor strip contact; a working electrode inelectrical communication with the first sensor strip contact; a counterelectrode in electrical communication with the second sensor stripcontact; and a first reagent layer on (i) the working electrode, (ii)the counter electrode, or (iii) both the working electrode and thecounter electrode, the first reagent layer including an oxidoreductaseand at least one species of a redox pair.
 2. The system of claim 1,wherein the analyte is glucose.
 3. The system of claim 1, wherein thefirst reagent layer is on both the working electrode and the counterelectrode.
 4. The system of claim 1, wherein the sensor strip furtherincludes a second reagent layer on at least the counter electrode, thesecond reagent layer including at least one species of a redox pair. 5.The system of claim 1, wherein the electrical circuitry includes acharger configured to apply the acyclic scan to the sensor strip, andwherein the sensor strip contains the sample.
 6. The system of claim 1,wherein the acyclic scanning comprises forward and reverse linear scans,the forward scan starting at a different voltage than where the reversescan stops.
 7. The system of claim 1, wherein the acyclic scan includesforward and reverse linear scans, the forward scan starting and thereverse scan ending at a point at most ±20 mV away from a formalpotential E°′ of a redox pair.
 8. The system of claim 1, wherein theacyclic scan includes forward and reverse linear scans within thesteady-state region of a redox pair, the forward and reverse scanshaving a scan range from 10 to 200 mV.
 9. A system for determining aconcentration of an analyte in a sample, comprising: a measuring deviceincluding at least two device contacts in electrical communication witha display through electrical circuitry, the measuring device beingconfigured to apply a voltammetric scan to the sample; and a sensorstrip receivable by the measuring device, the sensor strip including: afirst sensor strip contact; a second sensor strip contact; a workingelectrode in electrical communication with the first sensor stripcontact; a counter electrode in electrical communication with the secondsensor strip contact; and a first reagent layer on (i) the workingelectrode, the (ii) the counter electrode, or (iii) both the workingelectrode and the counter electrode, the first reagent layer includingan oxidoreductase and at least one species of a redox pair.
 10. Thesystem of claim 9, wherein the analyte is glucose.
 11. The system ofclaim 9, wherein the voltammetric scan includes a linear scan.
 12. Thesystem of claim 9, wherein the voltammetric scan includes a cyclic scan.13. The system of claim 9, wherein the first reagent layer is on boththe working electrode and the counter electrode.
 14. The system of claim9, wherein the first reagent layer is on the working electrode, andwherein the sensor strip further includes a second reagent layer on thecounter electrode, the second reagent layer including at least onespecies of a redox pair.
 15. The system of claim 9, wherein theelectrical circuitry includes a charger configured to apply thevoltammetric scan to the sensor strip, and wherein the sensor stripcontains the sample.
 16. The system of claim 9, wherein the charger isconfigured to apply a linear scan to the sensor strip.
 17. The system ofclaim 9, wherein the charger is configured to apply a cyclic scan to thesensor strip.